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By Fabien Anselmet, Pierre-Olivier Mattei

This didactic e-book offers the most parts of acoustics, aeroacoustics and vibrations.

Illustrated with a number of concrete examples associated with good and fluid continua, Acoustics, Aeroacoustics and Vibrations proposes a variety of purposes encountered within the 3 fields, no matter if in room acoustics, delivery, strength creation structures or environmental difficulties. Theoretical ways allow us to investigate the various strategies in play. regular effects, generally from numerical simulations, are used to demonstrate the most phenomena (fluid acoustics, radiation, diffraction, vibroacoustics, etc.).

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This thermoelastic relaxation time defines a crucial region in which the conduction process manages to balance the inequalities of temperature (isothermal or relaxed regime) or not (adiabatic or non-relaxed regime) during a vibration period. In the adiabatic regime, the thermal and the mechanical fields are in phase while in an isothermal regime, they are out of phase by 90◦ . In the transition area, these fields are out of phase by 45◦ and the damping is maximum. 6 This justifies the use of torsion clocks to measure the viscoelasticity of metals.

At high frequencies (beyond the pulse 1/τ ), the instantaneous modulus should be used. Zener has characterized this loss angle for thin metal structures. He has demonstrated that nearly 99% of the relaxation is brought by the first transverse thermal mode and that the relaxation time is then given by τ = (h/π)2 /D, where D is the thermal diffusivity with D = kθ /(ρcv ) m2 /s, where h is the thickness of the structure, cv is the specific heat per volume unit at constant strain and kθ is the thermal conductivity.

01. 10−6 K−1 . 002. 0001 [LES 88]. 6 ms. The frequency in the vicinity of which damping is maximal is f = 1/(2πτ ) ≈ 60 Hz. 0012). In addition, its thermal diffusivity, and thus the frequency at which it is maximal, is 4 times lower than for aluminum. In practice, for the dimensions that usually come across, it is fairly insignificant for acoustic phenomena (about 8 Hz for a 2 mm thick plate). 2. Convolution operator The convolution operator reflects a memory effect. At a given moment, this effect characterizes the dependence of the response to previous modifications whose respective importance is weighted by a relaxation kernel (or a function)14.

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